It's bewildering that the Photo app on the IPhone does not. I wonder what the reason behind that is.

It's different. Dropbox works with iCloud Drive. That's a good place to store photos. There's apps not connected to iCloud Drive that's are great photo storage apps. Box and OneDrive are great. You can back up and store all your photos to the ICloud Photo Library. And you can upload photos to iCloud Photo Sharing, if you want to create albums and share those with family. I gave photos there, but am not sharing yet.